Punctuated equilibrium as the default mode of evolution of large populations on fitness landscapes dominated by saddle points in the weak-mutation limit

Abstract

Punctuated equilibrium is a mode of evolution in which phenetic change occurs in rapid bursts that are separated by much longer intervals of stasis during which mutations accumulate but no major phenotypic change occurs. Punctuated equilibrium has been originally proposed within the framework of paleobiology, to explain the lack of transitional forms that is typical of the fossil record. Theoretically, punctuated equilibrium has been linked to self-organized criticality (SOC), a model in which the size of avalanches in an evolving system is power-law distributed, resulting in increasing rarity of major events. We show here that, under the weak-mutation limit, a large population would spend most of the time in stasis in the vicinity of saddle points in the fitness landscape. The periods of stasis are punctuated by fast transitions, in lnNe time (Ne, effective population size), when a new beneficial mutation is fixed in the evolving population, which moves to a different saddle, or on much rarer occasions, from a saddle to a local peak. Thus, punctuated equilibrium is the default mode of evolution under a simple model that does not involve SOC or other special conditions.

Quasi-species evolution maximizes genotypic reproductive value (not fitness or flatness)

“…The quasi-species equation (1) can be linearized by dropping the non-linear mean-fitness term , whose sole effect is to maintain normalization of densities. In this way (1) becomes similar to the parabolic Anderson model introduced by Zel’dovich et al as a model of intermittent dynamics [31]; indeed, one salient feature of quasi-species dynamics is its punctuated nature, with populations localizing in regions of the fitness landscapes for long transients before suddenly jumping to remote areas in bursts of rapid adaptation [32].…”